Answered: calculate a 90% CI for the average GPA…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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calculate a 90% CI for the average GPA of college students from a sample of 49 students with a mean GPA of 2.7 and a standard deviation of 0.1

1) What is the standard error?
2) What is the criticla z or t score ?
3) What is 90% CI?
4) If it is known the population SD of students' GPA is 0.2, what is the 90% CI?

Expert Solution

Introduction

{NOTE : As per the rules, only the first 3 subparts are solved. ]

Given that,

$n = 49 \bar{x} = 2.7 s = 0.1$

Standard Error = $\frac{s}{\sqrt{n}}$

The confidence level of population mean $(μ)$ at level $α$ , when the sample mean and sample standard deviation is given , is :

$\bar{x} - z_{\frac{α}{2}} \times \frac{s}{\sqrt{n}} ⩽ μ ⩽ \bar{x} + z_{\frac{α}{2}} \times \frac{s}{\sqrt{n}}$

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